### Iteration

It is often the case in programming – especially when dealing with randomness – that we want to repeat a process multiple times. For example, we might want to assign each person in a study to the treatment group or to control, based on tossing a coin. We can do this without actually tossing a coin for each person; we can just use `np.random.choice`

instead.

Here is a reminder of how `np.random.choice`

works. Run the cell a few times to see how the output changes.

```
np.random.choice(make_array('Heads', 'Tails'))
```

```
'Heads'
```

To come up with Heads or Tails for each individual in our study, we could copy-paste the code multiple times, but that’s tedious and prone to typos, and if we wanted to do it a thousand times or a million times, forget it.

A more automated solution is to use a `for`

statement to loop over the contents of a sequence. This is called *iteration*. A `for`

statement begins with the word `for`

, followed by a name we want to give each item in the sequence, followed by the word `in`

, and ending with an expression that evaluates to a sequence. The indented body of the `for`

statement is executed once *for each item in that sequence*.

```
for i in np.arange(3):
print(i)
```

```
0
1
2
```

It is instructive to imagine code that exactly replicates a `for`

statement without the `for`

statement. This is called *unrolling* the loop.

A `for`

statement simple replicates the code inside it, but before each iteration, it assigns a new value from the given sequence to the name we chose. For example, here is an unrolled version of the loop above:

```
i = np.arange(3).item(0)
print(i)
i = np.arange(3).item(1)
print(i)
i = np.arange(3).item(2)
print(i)
```

```
0
1
2
```

Notice that the name `i`

is arbitrary, just like any name we assign with `=`

.

Here we use a `for`

statement in a more realistic way: we print 5 random choices from `coin`

, thus *simulating* the results five tosses of a coin. We use the word *simulating* to remind ourselves that we are not physically tossing coins but using Python to mimic the process.

```
coin = make_array('Heads', 'Tails')
for i in np.arange(5):
print(np.random.choice(coin))
```

```
Heads
Heads
Heads
Tails
Heads
```

In this case, we simply perform exactly the same (random) action several times, so the code inside our `for`

statement does not actually refer to `i`

.

### Augmenting Arrays

While the `for`

statement above does simulate the results of five tosses of a coin, the results are simply printed and aren’t in a form that we can use for computation. Thus a typical use of a `for`

statement is to create an array of results, by augmenting it each time.

The `append`

method in `numpy`

helps us do this. The call `np.append(array_name, value)`

evaluates to a new array that is `array_name`

augmented by `value`

. When you use `append`

, keep in mind that all the entries of an array must have the same type.

```
pets = make_array('Cat', 'Dog')
np.append(pets, 'Another Pet')
```

```
array(['Cat', 'Dog', 'Another Pet'], dtype='<U11')
```

This keeps the array `pets`

unchanged:

```
pets
```

```
array(['Cat', 'Dog'], dtype='<U3')
```

But often while using `for`

loops it will be convenient to mutate an array – that is, change it – when augmenting it. This is done by assigning the augmented array to the same name as the original.

```
pets = np.append(pets, 'Another Pet')
pets
```

```
array(['Cat', 'Dog', 'Another Pet'], dtype='<U11')
```

### Example: Counting the Number of Heads

We can now simulate five tosses of a coin and place the results into an array. We will start by creating an empty array and then appending the outcome of each toss. Notice that the body of the `for`

loop contains two statements. Both statements are executed for each value in the given sequence `np.arange(5)`

.

```
coin = make_array('Heads', 'Tails')
outcomes = make_array()
for i in np.arange(5):
outcome_of_toss = np.random.choice(coin)
outcomes = np.append(outcomes, outcome_of_toss)
outcomes
```

```
array(['Tails', 'Tails', 'Tails', 'Heads', 'Tails'], dtype='<U32')
```

Let us rewrite the cell with the `for`

statement unrolled:

```
coin = make_array('Heads', 'Tails')
outcomes = make_array()
i = np.arange(5).item(0)
outcome_of_toss = np.random.choice(coin)
outcomes = np.append(outcomes, outcome_of_toss)
i = np.arange(5).item(1)
outcome_of_toss = np.random.choice(coin)
outcomes = np.append(outcomes, outcome_of_toss)
i = np.arange(5).item(2)
outcome_of_toss = np.random.choice(coin)
outcomes = np.append(outcomes, outcome_of_toss)
i = np.arange(5).item(3)
outcome_of_toss = np.random.choice(coin)
outcomes = np.append(outcomes, outcome_of_toss)
i = np.arange(5).item(4)
outcome_of_toss = np.random.choice(coin)
outcomes = np.append(outcomes, outcome_of_toss)
outcomes
```

```
array(['Heads', 'Heads', 'Heads', 'Tails', 'Heads'], dtype='<U32')
```

By capturing the results in an array we have given ourselves the ability to use array methods to do computations. For example, we can use `np.count_nonzero`

to count the number of heads in the five tosses.

```
np.count_nonzero(outcomes == 'Heads')
```

```
4
```

Keep in mind that we have used the `for`

loop to simulate a random experiment, and therefore if you run the cell again, the array `outcomes`

is likely to be different. In upcoming sections of the course we will study how different the outcomes could be.

Iteration is a powerful technique. For example, by running exactly the same code for 1000 tosses instead of 5, we can count the number of heads in 1000 tosses.

```
outcomes = make_array()
for i in np.arange(1000):
outcome_of_toss = np.random.choice(coin)
outcomes = np.append(outcomes, outcome_of_toss)
np.count_nonzero(outcomes == 'Heads')
```

```
515
```